-4-


and it.2 V/qi would represent an approximate 95 percent confidence

interval for the successive coefficient it+l"

 Clearly estimation of the varying parameters must be referenced to

some point during the sample period. Because interest is focused on

forecasting, we desire the value of the parameters given the most recent

observation. The values taken by the parameters given all observations

through the most recent will be denoted T*. To estimate BT, Sant (1977)

has formulated a generalized least squares model of the form

 YT = X TT + ET ATUT (4)


where

 X1 1X X1 X1 112

 AT = 0 x2. x2 x2 and UT= 3





 0 0 .0 xT-1 "lT-1

 0 0 0 0 0


 Alternatively (4) may be written compactly

 YT = XT8T + VT (5)


 Here YT and XT represent the customary TXl regressand vector and txk

 design matrix. The complex structure incorporated into the disturbance

 vector VT results from the successive solution of (2) in terms of BT"